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Mathematics LibreTexts

13.5.6E: Exercises

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Practice Makes Perfect

Find Equivalent Fractions

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

Exercise 13.5.6E.1

38

Answer

616, 924, 1232, answers may vary

Exercise 13.5.6E.2

58

Exercise 13.5.6E.3

59

Answer

1018, 1527, 2036, answers may vary

Exercise 13.5.6E.4

18

Simplify Fractions

In the following exercises, simplify.

Exercise 13.5.6E.5

4088

Answer

511

Exercise 13.5.6E.6

6399

Exercise 13.5.6E.7

10863

Answer

127

Exercise 13.5.6E.8

10448

Exercise 13.5.6E.9

120252

Answer

1021

Exercise 13.5.6E.10

182294

Exercise 13.5.6E.11

3x12y

Answer

x4y

Exercise 13.5.6E.12

4x32y

Exercise 13.5.6E.13

14x221y

Answer

2x23y

Exercise 13.5.6E.14

24a32b2

Multiply Fractions

In the following exercises, multiply.

Exercise 13.5.6E.15

34910

Answer

2740

Exercise 13.5.6E.16

4527

Exercise 13.5.6E.17

2338

Answer

14

Exercise 13.5.6E.18

34(49)

Exercise 13.5.6E.19

59310

Answer

16

Exercise 13.5.6E.20

38415

Exercise 13.5.6E.21

(1415)(920)

Answer

2150

Exercise 13.5.6E.22

(910)(2533)

Exercise 13.5.6E.23

(6384)(4490)

Answer

1130

Exercise 13.5.6E.24

(6360)(4088)

Exercise 13.5.6E.25

4511

Answer

2011

Exercise 13.5.6E.26

583

Exercise 13.5.6E.27

3721n

Answer

9n

Exercise 13.5.6E.28

5630m

Exercise 13.5.6E.29

8174

Answer

−34

Exercise 13.5.6E.30

(1)(67)

Divide Fractions

In the following exercises, divide.

Exercise 13.5.6E.31

34÷23

Answer

98

Exercise 13.5.6E.32

45÷34

Exercise 13.5.6E.33

79÷(74)

Answer

49

Exercise 13.5.6E.34

56÷(56)

Exercise 13.5.6E.35

34÷x11

Answer

334x

Exercise 13.5.6E.36

25÷y9

Exercise 13.5.6E.37

518÷1524

Answer

49

Exercise 13.5.6E.38

718÷(1427)

Exercise 13.5.6E.39

8u15÷12v25

Answer

10u9v

Exercise 13.5.6E.40

12r25÷18s35

Exercise 13.5.6E.41

5÷12

Answer

-10

Exercise 13.5.6E.42

3÷14

Exercise 13.5.6E.43

34÷(12)

Answer

116

Exercise 13.5.6E.44

15÷53

In the following exercises, simplify.

Exercise 13.5.6E.45

8211235

Answer

109

Exercise 13.5.6E.46

9163340

Exercise 13.5.6E.47

452

Answer

25

Exercise 13.5.6E.48

5310

Exercise 13.5.6E.49

m3n2

Answer

2m3n

Exercise 13.5.6E.50

38y12

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

Exercise 13.5.6E.51

22+310

Answer

52

Exercise 13.5.6E.52

1946

Exercise 13.5.6E.53

482415

Answer

163

Exercise 13.5.6E.54

464+4

Exercise 13.5.6E.55

6+68+4

Answer

0

Exercise 13.5.6E.56

6+3178

Exercise 13.5.6E.57

4366

Answer

13

Exercise 13.5.6E.58

6692

Exercise 13.5.6E.59

42125

Answer

35

Exercise 13.5.6E.60

72+160

Exercise 13.5.6E.61

83+2914+3

Answer

4217

Exercise 13.5.6E.62

964722+3

Exercise 13.5.6E.63

56344523

Answer

97

Exercise 13.5.6E.64

89765692

Exercise 13.5.6E.65

523235

Answer

8

Exercise 13.5.6E.66

624246

Exercise 13.5.6E.67

742(85)9335

Answer

116

Exercise 13.5.6E.68

973(128)8766

Exercise 13.5.6E.69

9(82)3(157)6(71)3(179)

Answer

52

Exercise 13.5.6E.70

8(92)4(149)7(83)3(169)

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

Exercise 13.5.6E.71

the quotient of r and the sum of s and 10

Answer

rs+10

Exercise 13.5.6E.72

the quotient of A and the difference of 3 and B

Exercise 13.5.6E.73

the quotient of the difference of x and y, and 3

Answer

xy3

Exercise 13.5.6E.74

the quotient of the sum of m and n, and 4q

Everyday Math

Exercise 13.5.6E.75

Baking. A recipe for chocolate chip cookies calls for 34 cup brown sugar. Imelda wants to double the recipe.

  1. How much brown sugar will Imelda need? Show your calculation.
  2. Measuring cups usually come in sets of 14, 13, 12, and 1 cup. Draw a diagram to show two different ways that Imelda could measure the brown sugar needed to double the cookie recipe.
Answer
  1. 112 cups
  2. answers will vary
Exercise 13.5.6E.76

Baking. Nina is making 4 pans of fudge to serve after a music recital. For each pan, she needs 23 cup of condensed milk.

  1. How much condensed milk will Nina need? Show your calculation.
  2. Measuring cups usually come in sets of 14, 13, 12, and 1 cup. Draw a diagram to show two different ways that Nina could measure the condensed milk needed for 4 pans of fudge.
Exercise 13.5.6E.77

Portions Don purchased a bulk package of candy that weighs 5 pounds. He wants to sell the candy in little bags that hold 14 pound. How many little bags of candy can he fill from the bulk package?

Answer

20 bags

Exercise 13.5.6E.78

Portions Kristen has 34 yards of ribbon that she wants to cut into 6 equal parts to make hair ribbons for her daughter’s 6 dolls. How long will each doll’s hair ribbon be?

Writing Exercises

Exercise 13.5.6E.79

Rafael wanted to order half a medium pizza at a restaurant. The waiter told him that a medium pizza could be cut into 6 or 8 slices. Would he prefer 3 out of 6 slices or 4 out of 8 slices? Rafael replied that since he wasn’t very hungry, he would prefer 3 out of 6 slices. Explain what is wrong with Rafael’s reasoning.

Answer

Answers may vary

Exercise 13.5.6E.80

Give an example from everyday life that demonstrates how 1223 is 13.

Exercise 13.5.6E.81

Explain how you find the reciprocal of a fraction.

Answer

Answers may vary

Exercise 13.5.6E.82

Explain how you find the reciprocal of a negative number.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

A table is shown that is made up of four columns and seven rows. The first row reads “I can…” in the first column, “Confidently” in the second column, “With some help” in the third column and “No – I don’t get it” in the last column. The next row down in the first column reads “find equivalent fractions”, under this reads “simplify fractions”, under this reads “multiply fractions”, under this reads “divide fractions”, under this reads “Simplify expressions written with a fraction bar” and under this reads “translate phrases to expressions with fractions.”

ⓑ After looking at the checklist, do you think you are well prepared for the next section? Why or why not?


This page titled 13.5.6E: Exercises is shared under a not declared license and was authored, remixed, and/or curated by OpenStax.

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